Answer:
Explanation:
a ) Momentum of first cart = mass x velocity
= 3 x 4.6 =+13.8 kg m /s
Momentum of second cart = 1.3 x - 1.9 = - 2.47 kg m /s
Total momentum = 13.8 - 2.47
= +11.33 kg m /s
b )
Let the velocity of first cart be v at the moment when second cart was at rest
total momentum = 3 x v + 0 = 3 v
Applying conservation of momentum law
3 v = +11.33
v = +3.77 m /s
Answer:
The radius of the new planet is ~2.04 * 10⁶ m, or 2,041,752 m.
Explanation:
We can use Newton's Law of Universal Gravitation:
Let's look at Newton's 2nd Law:
We can set these equations equal to each other:
The mass of the second mass (astronaut) cancels out. We are left with:
We are solving for the radius of the new planet, so we can rearrange the equation:
Substitute in our known values given in the problem (<u><em>G = 6.67 * 10⁻¹¹ </em></u><em> ; </em><u><em>M = 7.5 * 10²³</em></u><em> ; </em><u><em>a = 12</em></u>).
The radius of the new planet is ~2.04 * 10⁶ m.
When light travels from a medium with higher refractive index to a medium with lower refractive index, the critical angle is the angle of incidence above which light is reflected only (no refraction occurs), and the value of this critical angle is given by

where n2 is the refractive index of the second medium and n1 is the refractive index of the first medium.
In this problem, the first medium is the glass (

), while the second medium is oil (

), therefore the critical angle is given by